Infrared 🔥

Geometric Algebra for Mojo

-- Moving hybrid types to their own Moplex module, so not much to see here right now.

I'll start playing with some more GA like structures soon though. Big plans!

package layout:

• hybrid

(deprecated) hybrid example:

from infrared.hybrid import Hyplex, Complex, Paraplex
from infrared.io import _print

# define some unit antiscalars
alias x = Hyplex.I(1)
alias i = Complex.I(1)
alias o = Paraplex.I(1)

_print(x)      #: 1x
_print(x * x)  #: 1
_print()
_print(i)      #: 1i
_print(i * i)  #: -1
_print()
_print(o)      #: 1o
_print(o * o)  #: 0
_print()

rx = 0.5 + x
ri = 0.5 + i
ro = 0.5 + o

_print(rx)       #: 0.5 + 1x
_print(rx * rx)  #: 1.25 + 1x
_print()
_print(ri)       #: 0.5 + 1i
_print(ri * ri)  #: -0.75 + 1i
_print()
_print(ro)       #: 0.5 + 1o
_print(ro * ro)  #: 0.25 + 1o

Naming convention which is suggestive of what each basis element squares to:

hybrid:

signature	structure	name
G1	s - x	Hyplex
G01	s - i	Complex
G001	s - o	Paraplex

binumeral:

signature	structure	name
G2	s - v.x v.y - i
G02	s - v.i v.j - i	Quaterion
G002	s - v.o v.p - o
G11	s - v.x v.i - x
G101	s - v.o v.x - o
G011	s - v.o v.i - o

trinumeral:

signature	structure	name
G3	s - v.x v.y v.z - vv.i vv.j vv.k - i
G03	s - v.i v.j v.k - vv.i vv.j vv.k - x
G003	s - v.o v.p v.q - vv.o vv.p vv.q - o
G21	s - v.x v.y v.i - vv.i vv.x vv.y - x
G201	s - v.x v.y v.o - vv.i vv.o vv.p - o
G12	s - v.x v.i v.j - vv.x vv.y vv.i - i
G021	s - v.i v.j v.o - vv.i vv.o vv.p - o
G102	s - v.x v.o v.p - vv.o vv.p vv.q - o
G012	s - v.i v.o v.p - vv.o vv.p vv.q - o
G111	s - v.x v.i v.o - vv.x vv.o vv.p - o